1DLANGB(1)           LAPACK auxiliary routine (version 3.2)           DLANGB(1)
2
3
4

NAME

6       DLANGB  -  returns the value of the one norm, or the Frobenius norm, or
7       the infinity norm, or the element of largest absolute value of an n  by
8       n band matrix A, with kl sub-diagonals and ku super-diagonals
9

SYNOPSIS

11       DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB, WORK )
12
13           CHARACTER    NORM
14
15           INTEGER      KL, KU, LDAB, N
16
17           DOUBLE       PRECISION AB( LDAB, * ), WORK( * )
18

PURPOSE

20       DLANGB   returns  the value of the one norm,  or the Frobenius norm, or
21       the  infinity norm,  or the element of  largest absolute value  of an n
22       by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
23

DESCRIPTION

25       DLANGB returns the value
26          DLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
27                   (
28                   ( norm1(A),         NORM = '1', 'O' or 'o'
29                   (
30                   ( normI(A),         NORM = 'I' or 'i'
31                   (
32                   (  normF(A),          NORM  =  'F',  'f',  'E' or 'e' where
33       norm1  denotes the  one norm of a matrix (maximum  column  sum),  normI
34       denotes  the   infinity  norm  of a matrix  (maximum row sum) and normF
35       denotes the  Frobenius  norm  of  a  matrix  (square  root  of  sum  of
36       squares).   Note  that   max(abs(A(i,j)))   is  not a consistent matrix
37       norm.
38

ARGUMENTS

40       NORM    (input) CHARACTER*1
41               Specifies the value to  be  returned  in  DLANGB  as  described
42               above.
43
44       N       (input) INTEGER
45               The  order of the matrix A.  N >= 0.  When N = 0, DLANGB is set
46               to zero.
47
48       KL      (input) INTEGER
49               The number of sub-diagonals of the matrix A.  KL >= 0.
50
51       KU      (input) INTEGER
52               The number of super-diagonals of the matrix A.  KU >= 0.
53
54       AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
55               The band matrix A, stored in rows 1 to KL+KU+1.  The j-th  col‐
56               umn  of  A is stored in the j-th column of the array AB as fol‐
57               lows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
58
59       LDAB    (input) INTEGER
60               The leading dimension of the array AB.  LDAB >= KL+KU+1.
61
62       WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
63               where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐
64               enced.
65
66
67
68 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       DLANGB(1)